Asteroid 2015 DB216: a Recurring Co-Orbital Companion to Uranus
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MNRAS 453, 1288–1296 (2015) doi:10.1093/mnras/stv1725 Asteroid 2015 DB216: a recurring co-orbital companion to Uranus C. de la Fuente Marcos‹ and R. de la Fuente Marcos Apartado de Correos 3413, E-28080 Madrid, Spain Accepted 2015 July 27. Received 2015 July 7; in original form 2015 June 3 ABSTRACT Minor bodies trapped in 1:1 co-orbital resonances with a host planet could be relevant to explain the origin of captured satellites. Among the giant planets, Uranus has one of the smallest known Downloaded from populations of co-orbitals, three objects, and all of them are short-lived. Asteroid 2015 DB216 has an orbital period that matches well that of Uranus, and here we investigate its dynamical state. Direct N-body calculations are used to assess the current status of this object, reconstruct its immediate dynamical past, and explore its future orbital evolution. A covariance matrix- based Monte Carlo scheme is presented and applied to study its short-term stability. We find http://mnras.oxfordjournals.org/ that 2015 DB216 is trapped in a temporary co-orbital resonance with Uranus, the fourth known minor body to do so. A detailed analysis of its dynamical evolution shows that it is an unstable but recurring co-orbital companion to Uranus. It currently follows an asymmetric horseshoe trajectory that will last for at least 10 kyr, but it may remain inside Uranus’ co-orbital zone for millions of years. As in the case of other transient Uranian co-orbitals, complex multibody ephemeral mean motion resonances trigger the switching between the various resonant co- orbital states. The new Uranian co-orbital exhibits a secular behaviour markedly different from ◦ that of the other known Uranian co-orbitals because of its higher inclination, nearly 38 .Given at Northwestern University Library on February 2, 2016 its rather unusual discovery circumstances, the presence of 2015 DB216 hints at the existence of a relatively large population of objects moving in similar orbits. Key words: methods: numerical – methods: statistical – celestial mechanics – minor planets, asteroids: individual: 2015 DB216 – planets and satellites: individual: Uranus. et al. 2013; de la Fuente Marcos & de la Fuente Marcos 2014). Due 1 INTRODUCTION to its present short data-arc (85 d), 2010 EU65 is better described For over a century, co-orbitals – or minor bodies trapped in a 1:1 as a candidate. Asteroids Crantor and 2010 EU65 follow horse- mean motion resonance with a host planet – have been regarded as shoe orbits, and 2011 QF99 is an L4 Trojan. Consistently, Uranus mere interesting dynamical curiosities (Jackson 1913; Henon 1969; has also a small population of irregular satellites, significantly Namouni 1999). This view is now changing considerably; in fact, smaller than that of Jupiter or Saturn (Grav et al. 2003; Sheppard, the heliocentric 1:1 co-orbital resonance could be an efficient mech- Jewitt & Kleyna 2005). Most Uranian irregular satellites are ret- anism for capture of satellites by a planet and therefore explain the rograde and their large spread in semimajor axis suggest that they origin of some irregular moons (Kortenkamp 2005). This theoretical formed independently (Nesvornyetal.´ 2003); orbits with inclina- possibility – that of being a feasible dynamical pathway to capture tions in the range (80◦, 100◦) are unstable due to the Kozai resonance satellites, at least temporarily – was dramatically vindicated when (Kozai 1962). For the particular case of Uranus’ Trojans, Dvorak, a co-orbital of the Earth, 2006 RH120, remained as natural satellite Bazso´ & Zhou (2010) have also found that the stability depends of our planet for about a year starting in 2006 June (Kwiatkowski on the orbital inclination and only the inclination intervals (0◦,7◦), et al. 2009; Granvik, Vaubaillon & Jedicke 2012). (9◦,13◦), (31◦,36◦), and (38◦,50◦) seem to be stable. Asteroid Uranus has one of the smallest known populations of co-orbitals 2011 QF99 appears to inhabit one of these stable islands at an incli- and all of them are relatively short-lived (de la Fuente Marcos & de nation of nearly 11◦ (de la Fuente Marcos & de la Fuente Marcos la Fuente Marcos 2014). So far, Uranus had only three known co- 2014). The stability of Uranian Trojans had been previously studied orbitals: 83982 Crantor (2002 GO9) (Gallardo 2006; de la Fuente by Marzari, Tricarico & Scholl (2003), and by Nesvorny´ & Dones Marcos & de la Fuente Marcos 2013), 2010 EU65 (de la Fuente Mar- (2002) and Holman & Wisdom (1993) before them. cos & de la Fuente Marcos 2013), and 2011 QF99 (Alexandersen Here, we present a recently discovered object, 2015 DB216,that is also trapped in a 1:1 mean motion resonance with Uranus. This minor body exhibits some dynamical features that separate it from E-mail: [email protected] the previously known Uranian co-orbitals. This paper is organized C 2015 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society A recurring co-orbital to Uranus 1289 Table 1. Heliocentric Keplerian orbital elements of 2015 DB216 used elements provided by the JPL On-line Solar System Data Service3 in this research. The orbit is based on 28 observations spanning (Giorgini et al. 1996) and initial positions and velocities based on a data-arc of 4200 d or 11.50 yr, from 2003 October 21 to 2015 the DE405 planetary orbital ephemerides (Standish 1998) referred April 23. Values include the 1σ uncertainty. The orbit is computed to the barycentre of the Solar system. Besides the orbital calcula- at epoch JD 245 7000.5 that corresponds to 0:00 UT on 2014 December 9 (J2000.0 ecliptic and equinox) and it is t = 0 in the figures. Source: tions completed using the nominal elements in Table 1,wehave JPL Small-Body Database. performed 50 control simulations with sets of orbital elements ob- tained from the nominal ones as described in the following section, Semimajor axis, a (au) = 19.204 ± 0.005 all of them for 0.5 Myr forward and backwards in time. Two more Eccentricity, e = 0.323 95 ± 0.000 13 sets of 100 control orbits each have been integrated for just 5 kyr into Inclination, i (◦) = 37.7173 ± 0.0003 the past and the future to better characterize its short-term stability. Longitude of the ascending node, (◦) = 6.2679 ± 0.0003 Argument of perihelion, ω (◦) = 237.75 ± 0.03 Mean anomaly, M (◦) = 302.52 ± 0.04 3 GENERATING CONTROL ORBITS Perihelion, q (au) = 12.9832 ± 0.0013 WITH MONTE CARLO AND THE Aphelion, Q (au) = 25.426 ± 0.007 COVARIANCE MATRIX Absolute magnitude, H (mag) = 8.3 ± 0.4 Downloaded from For a given minor body, the orbital elements are a coordinate in six- dimensional space (assuming as we do that non-gravitational forces can be neglected), which represents the location where samples of as follows. In Section 2, we briefly discuss both the data and the control orbits are most likely to be generated. This is analogous to the peak of the Gaussian curve for a typical one-dimensional or numerical model used in our calculations. The topic of generating http://mnras.oxfordjournals.org/ control orbits compatible with the available observations and its univariate normal distribution. The multivariate normal distribution implications is considered in Section 3. The current status of 2015 is a generalization of the one-dimensional normal distribution to higher dimensions. Instead of being specified by its mean value and DB216 is studied in Section 4, where its dynamical past and future orbital evolution are also investigated. Section 5 discusses our re- variance, such a distribution is characterized by its mean (a vector sults and their possible significance. The stability of the co-orbital with the mean of the multidimensional distribution) and covariance matrix, which defines a hyperellipsoid in multidimensional space. realm located in the neighbourhood of 2015 DB216 is tentatively explored in Section 6. A summary of our conclusions is given in The values of the elements of the covariance matrix indicate the Section 7. level to which two given variables vary together. For a particular object, both mean and covariance matrix are computed from the observations. at Northwestern University Library on February 2, 2016 2 DATA AND METHODOLOGY When studying the stability of the orbital solution of a certain minor planet, we can compute the orbital elements of the con- Asteroid 2015 DB216 was discovered on 2015 February 27 at Mt trol orbits varying them randomly, within the ranges defined by = Lemmon Survey. With a value of the semimajor axis a 19.20 au, their mean values and standard deviations. For example, a new = this Centaur moves in an eccentric, e 0.32, and highly inclined value of the orbital eccentricity can be found using the expression path, i = 37◦.72. With such an orbit, close encounters are only pos- ec = e + σ e ri,whereec is the eccentricity of the control orbit, e is sible with Uranus as its perihelion is well beyond Saturn’s aphelion the mean value of the eccentricity (nominal orbit), σ e is the standard and its aphelion far from Neptune’s perihelion. It is a relatively deviation of e (nominal orbit), and r is a (pseudo) random number = i large object with H 8.3 mag which translates into a diameter in with normal distribution in the range −1 to 1. In statistical terms, the range 46–145 km for an assumed albedo of 0.40–0.04. Its period the univariate Gaussian distribution results from adding a standard of revolution around the Sun, approximately 84.16 yr at present, is Gaussian variate with mean zero and variance one multiplied by the very close to that of Uranus which is suggestive of an object that standard deviation, to the mean value.